Let r(t) = (t² + 2)i + e ^t j + (12 + e ^t )k. Find N(t) for t = 0.

Question

Quizplus · Accepted Answer

To find the normal vector, we need to take the cross product of the tangent vectors in the direction of i and j, respectively. r(t) = (t² + 2)i + e ^t j + (12 + e ^t )k r'(t) = (²)i + (e )j + (e )k Taking the cross product of r'(0) with the vector in the direction of j: r'(0) x j = (-e ) i + (²) k Normalizing this vector, we get: N(t) = (-e /((e )^2 + (²)^2)^(1/2)) i + 0 j + (²/((e )^2 + (²)^2)^(1/2)) k Plugging in t=0 and simplifying leads to the answer A.

Let R(t) = (T2 + 2)i + E t J

Let R(t) = (T² + 2)i + E ^t J